arXiv subjects

Steven G. Johnson

Publications and source records attributed to Steven G. Johnson.

At least 37 records · Page 2Linked to original sources

arXiv2025

Unifying and accelerating level-set and density-based topology optimization by subpixel-smoothed projection

We introduce a new "subpixel-smoothed projection" (SSP) formulation for differentiable binarization in topology optimization (TopOpt) as a drop-in replacement for previous projection schemes, which suffer from near-non-differentiability and slow convergence as binarization improves. Our new algorithm overcomes these limitations by depending on both the underlying filtered design field and its spatial gradient, instead of the filtered design field alone. We can now smoothly transition between density-based TopOpt (in which topology can easily change during optimization) and a level-set method (in which shapes evolve in an almost-everywhere binarized structure). We demonstrate the effectiveness of our method on several photonics inverse-design problems and for a variety of computational methods (finite difference, Fourier-modal, and finite-element methods). SSP exhibits both faster convergence and greater simplicity.

physics.optics↗

arXiv2025

Time-reversal-symmetry bounds on electromagnetic fields

For linear electromagnetic systems possessing time-reversal symmetry, we present an approach to bound ratios of internal fields excited from different ports, using only the scattering matrix (S matrix), improving upon previous related bounds by Sounas and Alù (2017) [Phys. Rev. Lett. 118, 154302 (2017)]. By reciprocity, emitted-wave amplitudes from internal dipole sources are bounded in a similar way. When applied to coupled-resonant systems, our method constrains ratios of resonant coupling/decay coefficients. We also obtain a relation for the relative phase of fields excited from the two ports and the ratio of field intensities in a two-port system. In addition, although lossy systems do not have time-reversal symmetry, we can still approximately bound loss-induced non-unitarity of the S matrix using only the lossless S matrix. We show numerical validations of the near-tightness of our bounds in various scattering systems.

physics.optics↗

arXiv2025

Scalable freeform optimization of wide-aperture 3D metalenses by zoned discrete axisymmetry

We introduce a novel framework for design and optimization of 3D freeform metalenses that attains nearly linear scaling of computational cost with diameter, by breaking the lens into a sequence of radial "zones" with $n$-fold discrete axisymmetry, where $n$ increases with radius. This allows vastly more design freedom than imposing continuous axisymmetry, while avoiding the compromises of the locally periodic approximation (LPA) or scalar diffraction theory. Using a GPU-accelerated finite-difference time-domain (FDTD) solver in cylindrical coordinates, we perform full-wave simulation and topology optimization within each supra-wavelength zone. We validate our approach by designing millimeter and centimeter-scale, poly-achromatic, 3D freeform metalenses which outperform the state of the art. By demonstrating the scalability and resulting optical performance enabled by our "zoned discrete axisymmetry" (ZDA) and supra-wavelength domain decomposition, we highlight the potential of our framework to advance large-scale meta-optics and next-generation photonic technologies.

physics.optics↗

arXiv2025

Efficient inverse design of large-area metasurfaces for incoherent light

Incoherent light is ubiquitous, yet designing optical devices that can handle its random nature is very challenging, since directly averaging over many incoherent incident beams can require a huge number of scattering calculations. We show how to instead solve this problem with a reciprocity technique which leads to three orders of magnitude speedup: one Maxwell solve (using any numerical technique) instead of thousands. This improvement enables us to perform efficient inverse design, large scale optimization of the metasurface for applications such as light collimators and concentrators. We show the impact of the angular distribution of incident light on the resulting performance, and show especially promising designs for the case of "annular" beams distributed only over nonzero angles.

physics.optics↗

arXiv2025

Inverse design of 3D-printable metalenses with complementary dispersion for terahertz imaging

This study formulates a volumetric inverse-design methodology to generate a pair of complementary focusing metalenses for terahertz imaging: the two lenses exhibit equal and opposite shifts in focal length with frequency. An asymmetry arises, where we find a focal length that decreases with frequency to be more challenging to achieve (without material dispersion) given fabrication constraints, but it is still possible. We employ topology optimization, coupled with manufacturing constraints, to explore fully freeform designs compatible with 3D printing. Formulating an optimization problem that quantifies the goal of maximal complementary focal shifts, while remaining differentiable and tractable, requires a carefully selected sequence of constraints and approximations.

physics.optics↗

arXiv2025

Sum-of-Squares Bounds on Surface-Enhanced Raman Scattering

Surface-enhanced Raman scattering (SERS) is a critical tool for chemical sensing and spectroscopy, and a key question is how to optimally design nanostructures for maximizing SERS. We present fundamental limits on spatially-averaged SERS via periodic metasurfaces, derived using sum-of-squares (SOS) programming. This work represents the first use of SOS techniques to optics, overcoming difficulties that prior bounding techniques have with regards to non-linear photonic processes with higher order figures of merit. Our bounds on the $\int \lVert \mathbf{E} \rVert^4 \text{d} \mathbf{r}$ SERS enhancement factor for 2D examples demonstrate remarkable tightness when compared with inverse-designed dielectric and metallic structures for both electrical field out-of-plane ($E_z$) and in-plane ($H_z$) polarizations. We show that delocalized high-Q guided modes can achieve significant, theoretically diverging SERS enhancement even in the presence of material loss. For metallic structures, we demonstrate a fundamental performance limitation for $E_z$ polarized drive fields due to surface plasmon excitation restrictions. By varying the separation between Raman-active molecules and the metasurface design region, we also find material-dependent bounds on the maximum strength of field singularities. Our results offer insights into optimal metasurface design strategies for enhancing light-matter interactions, and our methodology may be adapted to the study of other nonlinear photonics design problems.

physics.optics↗

arXiv2025

End-to-end metasurface design for temperature imaging via broadband Planck-radiation regression

We present a theoretical framework for temperature imaging from long-wavelength infrared thermal radiation (e.g. 8-12 $μ$m) through the end-to-end design of a metasurface-optics frontend and a computational-reconstruction backend. We introduce a new nonlinear reconstruction algorithm, ``Planck regression," that reconstructs the temperature map from a grayscale sensor image, even in the presence of severe chromatic aberration, by exploiting blackbody and optical physics particular to thermal imaging. We combine this algorithm with an end-to-end approach that optimizes a manufacturable, single-layer metasurface to yield the most accurate reconstruction. Our designs demonstrate high-quality, noise-robust reconstructions of arbitrary temperature maps (including completely random images) in simulations of an ultra-compact thermal-imaging device. We also show that Planck regression is much more generalizable to arbitrary images than a straightforward neural-network reconstruction, which requires a large training set of domain-specific images.

physics.optics↗

arXiv2025

Matrix Calculus (for Machine Learning and Beyond)

This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and return a matrix inverse or factorization, derivatives of ODE solutions, and even stochastic derivatives of random functions. It emphasizes practical computational applications, such as large-scale optimization and machine learning, where derivatives must be re-imagined in order to be propagated through complicated calculations. The class also discusses efficiency concerns leading to "adjoint" or "reverse-mode" differentiation (a.k.a. "backpropagation"), and gives a gentle introduction to modern automatic differentiation (AD) techniques.

math.HO↗

arXiv2024

End-to-End Optimization of Metasurfaces for Imaging with Compressed Sensing

We present a framework for the end-to-end optimization of metasurface imaging systems that reconstruct targets using compressed sensing, a technique for solving underdetermined imaging problems when the target object exhibits sparsity (i.e. the object can be described by a small number of non-zero values, but the positions of these values are unknown). We nest an iterative, unapproximated compressed sensing reconstruction algorithm into our end-to-end optimization pipeline, resulting in an interpretable, data-efficient method for maximally leveraging metaoptics to exploit object sparsity. We apply our framework to super-resolution imaging and high-resolution depth imaging with a phase-change material. In both situations, our end-to-end framework computationally discovers optimal metasurface structures for compressed sensing recovery, automatically balancing a number of complicated design considerations to select an imaging measurement matrix from a complex, physically constrained manifold with millions ofdimensions. The optimized metasurface imaging systems are robust to noise, significantly improving over random scattering surfaces and approaching the ideal compressed sensing performance of a Gaussian matrix, showing how a physical metasurface system can demonstrably approach the mathematical limits of compressed sensing.

eess.IV↗

arXiv2024

Towards optimal spatiotemporal wavefront shaping for the cocktail party problem with inverse design of an acoustic reconfigurable metasurface in disordered media

Multiple-user multiple-input multiple-output applications have recently gained a lot of attention. Here, we show an efficient optimization formulation for the design of all the temporal and spatial degrees of freedom of an acoustic reconfigurable metasurface for the cocktail party problem. In the frequency domain, the closed-form least square solution matches the optimal time reversal solution for multiple emitter-receiver pairs, optimizing for each frequency independently. This is more efficient than solving in the time domain where the time convolution mixes all the degrees of freedom into a resource-intensive optimization. We illustrate this methodology by optimizing the frequency response of a design for two pairs of emitters-receivers using the Green's functions of disordered media that are measured experimentally. We report strong performance that will be put in perspective in future work, where we will analyze the robustness of the design to noise in the data and design the convolutional filters that match the optimal frequency response for experiment validation of the design.

physics.app-ph↗

arXiv2023

Physics-enhanced deep surrogates for partial differential equations

Many physics and engineering applications demand Partial Differential Equations (PDE) property evaluations that are traditionally computed with resource-intensive high-fidelity numerical solvers. Data-driven surrogate models provide an efficient alternative but come with a significant cost of training. Emerging applications would benefit from surrogates with an improved accuracy-cost tradeoff, while studied at scale. Here we present a "physics-enhanced deep-surrogate" ("PEDS") approach towards developing fast surrogate models for complex physical systems, which is described by PDEs. Specifically, a combination of a low-fidelity, explainable physics simulator and a neural network generator is proposed, which is trained end-to-end to globally match the output of an expensive high-fidelity numerical solver. Experiments on three exemplar testcases, diffusion, reaction-diffusion, and electromagnetic scattering models, show that a PEDS surrogate can be up to 3$\times$ more accurate than an ensemble of feedforward neural networks with limited data ($\approx 10^3$ training points), and reduces the training data need by at least a factor of 100 to achieve a target error of 5%. Experiments reveal that PEDS provides a general, data-driven strategy to bridge the gap between a vast array of simplified physical models with corresponding brute-force numerical solvers modeling complex systems, offering accuracy, speed, data efficiency, as well as physical insights into the process.

cs.LG↗

arXiv2023

Efficient perturbative framework for coupling of radiative and guided modes in nearly periodic surfaces

We present a semi-analytical framework for computing the coupling of radiative and guided waves in slowly varying (nearly uniform or nearly periodic) surfaces, which is especially relevant to the exploitation of nonlocal effects in large-area metasurfaces. Our framework bridges a gap in the theory of slowly varying surfaces: aside from brute-force numerical simulations, current approximate methods can model either guided or radiative waves, but cannot easily model their coupling. We solve this problem by combining two methods: the locally periodic approximation, which approximates radiative scattering by composing a set of periodic scattering problems, and spatial coupled-wave theory, which allows the perturbative modeling of guided waves using an eigenmode expansion. We derive our framework for both nearly uniform and nearly periodic surfaces, and we validate each case against brute-force finite-difference time-domain simulations, which show increasing agreement as the surface varies more slowly.

physics.optics↗

arXiv2023

Transcending shift-invariance in the paraxial regime via end-to-end inverse design of freeform nanophotonics

Traditional optical elements and conventional metasurfaces obey shift-invariance in the paraxial regime. For imaging systems obeying paraxial shift-invariance, a small shift in input angle causes a corresponding shift in the sensor image. Shift-invariance has deep implications for the design and functionality of optical devices, such as the necessity of free space between components (as in compound objectives made of several curved surfaces). We present a method for nanophotonic inverse design of compact imaging systems whose resolution is not constrained by paraxial shift-invariance. Our method is end-to-end, in that it integrates density-based full-Maxwell topology optimization with a fully iterative elastic-net reconstruction algorithm. By the design of nanophotonic structures that scatter light in a non-shift-invariant manner, our optimized nanophotonic imaging system overcomes the limitations of paraxial shift-invariance, achieving accurate, noise-robust image reconstruction beyond shift-invariant resolution.

physics.optics↗

arXiv2022

Nonlinear exceptional-point lasing with ab-initio Maxwell-Bloch theory

We present a general analysis for finding and characterizing nonlinear exceptional point (EP) lasers above threshold, using steady-state ab-initio Maxwell-Bloch equations. For a system of coupled slabs, we show that a nonlinear EP is obtained for a given ratio between the external pumps in each resonator, and that it is associated with a kink in the output power and lasing frequency, confirming coupled-mode theory predictions. Through numerical linear stability analysis, we confirm that the EP laser can be stable for a large enough inversion relaxation rate. We further show that the EP laser can be characterized by scattering a weak signal off the lasing cavity, so that the scattering frequency spectrum exhibits a quartic divergence. Our approach can be applied to arbitrary scatterers with multi-level gain media.

physics.optics↗

arXiv2022

Inverse-designed lithium niobate nanophotonics

Lithium niobate-on-insulator (LNOI) is an emerging photonic platform that exhibits favorable material properties (such as low optical loss, strong nonlinearities, and stability) and enables large-scale integration with stronger optical confinement, showing promise for future optical networks, quantum processors, and nonlinear optical systems. However, while photonics engineering has entered the era of automated "inverse design" via optimization in recent years, the design of LNOI integrated photonic devices still mostly relies on intuitive models and inefficient parameter sweeps, limiting the accessible parameter space, performance, and functionality. Here, we develop and implement a 3D gradient-based inverse-design model tailored for topology optimization of the LNOI platform, which not only could efficiently search a large parameter space but also takes into account practical fabrication constraints, including minimum feature sizes and etched sidewall angles. We experimentally demonstrate a spatial-mode multiplexer, a waveguide crossing, and a compact waveguide bend, all with low insertion losses, tiny footprints, and excellent agreement between simulation and experimental results. The devices, together with the design methodology, represent a crucial step towards the variety of advanced device functionalities needed in future LNOI photonics, and could provide compact and cost-effective solutions for future optical links, quantum technologies and nonlinear optics.

physics.optics↗

arXiv2022

Automated Discovery and Optimization of 3D Topological Photonic Crystals

Topological photonic crystals have received considerable attention for their ability to manipulate and guide light in unique ways. They are typically designed by hand based on careful analysis of their bands and mode profiles, but recent theoretical advances have revealed new and powerful insights into the connection between band symmetry, connectivity, and topology. Here we propose a combined global and local optimization framework that integrates a flexible symmetry-constrained level-set parameterization with standard gradient-free optimization algorithms to optimize topological photonic crystals, a problem setting where the objective function may be highly non-convex and non-continuous. Our framework can be applied to any symmetry-identifiable band topology, and we demonstrate its applicability to several prominent kinds of three-dimensional band topology, namely $Γ$-enforced nodal lines, Weyl points, and Chern insulators. Requiring no prior examples of topological photonic crystals or prior knowledge on the connection between structure and band topology, our approach indicates a path towards the automated discovery of novel topological photonic crystal designs.

physics.optics↗

arXiv2022

Trace formulation for photonic inverse design with incoherent sources

Spatially incoherent light sources, such as spontaneously emitting atoms, naively require Maxwell's equations to be solved many times to obtain the total emission, which becomes computationally intractable in conjunction with large-scale optimization (inverse design). We present a trace formulation of incoherent emission that can be efficiently combined with inverse design, even for topology optimization over thousands of design degrees of freedom. Our formulation includes previous reciprocity-based approaches, limited to a few output channels (e.g. normal emission), as special cases, but generalizes to a continuum of emission directions by exploiting the low-rank structure of emission problems. We present several examples of incoherent-emission topology optimization, including tailoring the geometry of fluorescent particles, a periodically emitting surface, and a structure emitting into a waveguide mode, as well as discussing future applications to problems such as Raman sensing and cathodoluminescence.

physics.optics↗

arXiv2022

Inverse Design in Nanoscale Heat Transport via Interpolating Interfacial Phonon Transmission

We introduce a methodology for density-based topology optimization of non-Fourier thermal transport in nanostructures, based upon adjoint-based sensitivity analysis of the phonon Boltzmann transport equation (BTE) and a novel material interpolation technique, the "transmission interpolation model" (TIM). The key challenge in BTE optimization is handling the interplay between real- and momentum-resolved material properties. By parameterizing the material density with an interfacial transmission coefficient, TIM is able to recover the hard-wall and no-interface limits, while guaranteeing a smooth transition between void and solid regions. We first use our approach to tailor the effective thermal-conductivity tensor of a periodic nanomaterial; then, we maximize classical phonon size effects under constrained diffusive transport, identifying a promising new thermoelectric material design. Our method enables the systematic optimization of materials for heat management and conversion and, more broadly, the design of devices where diffusive transport is not valid.

cond-mat.mes-hall↗